Transition Probability of Hydrogen atom in an electric field

1. Dec 6, 2012

jmm5872

A hydrogen atom is in its ground state and is subject to an external electric field of

E = ε($\hat{x}$+$\hat{y}$+2$\hat{z}$)e-t/$\tau$

I'm confused as to how to compute the matrix elements of the perturbed hamiltonian since this is not in the z direction.

Would I have to do something like this?

H'ba = -pE = -qεe-t/$\tau$<$\psi$b|($\hat{x}$+$\hat{y}$+2$\hat{z}$)|$\psi$a>

Thanks

2. Dec 7, 2012

diazona

If I remember this stuff correctly, then yes. You're just using a unit vector in the direction of the electric field rather than in the z direction. Alternatively, you could rotate your coordinate system so that the electric field points in the z direction, solve the problem, and then rotate your solution back to the original coordinates.

3. Dec 7, 2012

TSny

Shouldn't you take the dot product of the electric field with the dipole moment vector operator: $\vec{p} = q\vec{r}= q(x \hat{x} + y \hat{y}+z \hat{z})$?

4. Dec 7, 2012

diazona

Oh yes, somehow I completely missed the fact that there was no dot product in the original post.